| Abstract: |
| In the first part of this talk, we derive a fully averaged poroelastic plate model. We discuss the existence of weak and mild solutions using a semigroup approach and propose a splitting scheme for the numerical analysis, comparing our model to existing poroelastic plate models.
The second part of the talk addresses the interaction problem of the fully averaged plate model with a Stokes fluid. We first prove the existence of weak solutions using energy methods and then show the existence of a unique strong solution to a regularized version of the problem. This is achieved by establishing the sectoriality of the associated operator matrix with a non-diagonal domain, thereby paving the way for maximal $\mathrm{L}^p$-regularity of the corresponding Cauchy problem. Finally, we derive a finite element method for the numerical approximation of the coupled problem and demonstrate its effectiveness in capturing the interaction between the fluid and the poroelastic plate.
This talk is based on joint work with S. \v{C}ani\`c, A. Scharf, and J. Tamba\v{c}a. |
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